The Production Routing Problem Under Uncertain Environment

To reduce waste and cost as well as to promote the efficient and sustainable use of resources in supply chains, a common focus of practice and research is to integrate decisions of various operational processes such as production, inventory, distribution, and routing. The question of which is more representative of the production routing problem (PRP) then arises. In this paper, the focus is on uncertainty in the PRP, and demand and cost uncertainty are considered simultaneously. According to different decision criteria, three uncertain programming models are correspondingly formulated. Then, through researching the crisp equivalence and conversion of the proposed uncertain models, a series of crisp equivalent models are proposed under the assumptions of particular uncertainty distributions, such as linear, zigzag, and normal distributions. To verify the accuracy and usefulness of the proposed models put forward in this paper, a series of experiments are conducted. Finally, several interesting managerial aspects with respect to the relationship between the confidence level and variance of uncertain variables that are gained from the numerical experiments are highlighted. First, the overall cost of PRP grows as the confidence level increases under uncertain environment. Second, the probability that the optimal total cost of the PRP is less than or equal to a given threshold strictly increases as the threshold increases under uncertain environment. Third, in circumstances such as higher confidence level that decision makers generally pay more attention to, the growth of the variance of uncertain variables may lead to the increase of the total cost.